With the development of quantum information processing, multipartite entanglement measures are needed in many cases. However, there are still no complete orthogonal genuine multipartite entanglement (GME) bases available as Bell states to bipartite systems. To achieve this goal, we find a method to construct complete orthogonal GME states, and we exclude many equivalent states by leveraging the group theory. We also provide the case of a $3$-order $3$-dimensional Hilbert space as an example and study the application of general results in the dense coding scheme as an application. Moreover, we discuss some open questions and believe that this work will enlighten extensive studies in this field.

We propose a model for a three-terminal quantum well heat engine with heat leakage. According to the Landauer formula, the expressions for the charge current, the heat current, the power output and the efficiency are derived in the linear-response regime. The curves of the power output and the efficiency versus the positions of energy levels and the bias voltage are plotted by numerical calculation. Moreover, we obtain the maximum power output and the corresponding efficiency, and analyze the influence of the heat leakage factor, the positions of energy levels and the bias voltage on these performance parameters.

At low four-momentum transfer squared $0.02 < -t < 0.2$ (GeV/$c$)$^{2}$, we use the Chou–Yang model to predict the form factor of protons from proton–proton elastic scattering at center-of-mass energy $\sqrt s=8$ TeV. By fitting differential cross-sectional data from the TOTEM experiment to a single Gaussian, the form factor is extracted. We use this form factor to find the rms matter radius of the proton to be 0.88 fm, which is in good agreement with the experimental data and the theoretically predicted values of the rms radius.

The nucleonic $^{1}S_{0}$ superfluidity is investigated by solving the gap equation for the Reid soft-core potential as the nucleon–nucleon interaction in neutron star (NS) matter which is considered to be made up of n, p, e, $\mu$ and condensed antikaon matter. We mainly study the influence of the soft pion-induced potential on the nucleonic $^{1}S_{0}$ pairing gaps in the above NS matter. It is found that the intensities of the nucleonic $^{1}S_{0}$ pairing gaps including the soft pion-induced potential are smaller than those calculated in the case of not including the soft pion-induced potential. Furthermore, the nucleonic $^{1}S_{0}$ pairing gaps with the soft pion-induced potential fall into decline with the deepening of the optical potential of antikaons in the above NS matter, whereas they increase with the parameter $\eta$ for the fixed optical potential of antikaons. Due to the appearance of the soft pion-induced potential, the maximum values of nucleonic $^{1}S_{0}$ pairing gaps at parameter $\eta=0.20, 0.55$ are suppressed by 1.7%–6.8% with respect to the case without soft pion-induced potential in the above NS matter.

Long-Chun Tao, Y. Ichikawa, Cen-Xi Yuan, Y. Ishibashi, A. Takamine, A. Gladkov, T. Fujita, K. Asahi, T. Egami, C. Funayama, K. Imamura, Jian-Ling Lou, T. Kawaguchi, S. Kojima, T. Nishizaka, T. Sato, D. Tominaga, Xiao-Fei Yang, H. Yamazaki, Yan-Lin Ye, H. Ueno

Traditional "magic numbers" were once regarded as immutable throughout the nuclear chart. However, unexpected changes were found for unstable nuclei around $N=20$. With both proton and neutron numbers around the magic number of 20, the neutron-rich $^{39}$Cl isotope provides a good test case for the study of the quantum-state evolution across the major shell. In the present work, the negative parity states in $^{39}$Cl are investigated through the $\beta$ decay spectroscopy of $^{39}$S. Newly observed $\gamma$ transitions together with a new state are assigned into the level scheme of $^{39}$Cl. The spin parity of ${5/2}^{-}$ for the lowest negative parity state in $^{39}$Cl is reconfirmed using the combined $\gamma$ transition information. These systematic observations of the negative parity states in $^{39}$Cl allow a comprehensive comparison with the theoretical descriptions. The lowest ${5/2}^{-}$ state in $^{39}$Cl remains exotic in terms of comparisons with existing theoretical calculations and with the neighboring isotopes having similar single-particle configurations. Further experimental and theoretical investigations are suggested.

A new observable, the angle between ${\it \Lambda}$ and $\bar{\it \Lambda}$ decay planes, is proposed to test the theoretical predictions on the spin correlation. With 10 billion $J/\psi$ events collected with the BESIII detector at the BEPCII $e^+e^-$ collider, the distribution of the angle could be measured to verify whether or not a correlation exists.

As a crucial parameter for a few-cycle laser pulse, the carrier envelope phase (CEP) substantially determines the laser waveform. We propose a method to directly describe the CEP of an isolated attosecond pulse (IAP) by the vortex-shaped momentum pattern, which is generated from the tunneling ionization of a hydrogen atom by a pair of time-delayed, oppositely and circularly polarized IAP-IR pulses. Superior to the angular streaking method that characterizes the CEP in terms of only one streak, our method describes the CEP of an IAP by the features of multiple streaks in the vortex pattern. The proposed method may open the possibility of capturing sub-cycle extreme ultraviolet dynamics.

FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS)

We experimentally investigate the continuous-wave (cw) and acousto-optical (AO) Q-switched performance of a diode-pumped Ho:(Sc$_{0.5}$Y$_{0.5})_{2}$SiO$_{5}$ (Ho:SYSO) laser. A fiber-coupled laser diode at 1.91 μm is employed as the pump source. The cw Ho:SYSO laser produces 13.0 W output power at 2097.9 nm and 56.0% slope efficiency with respect to the absorbed pump power. In the AO Q-switched regime, at a pulse repetition frequency of 5 kHz, the Ho:SYSO laser yields 2.1 mJ pulse energy and 21 ns pulse width, resulting in a calculated peak power of 100 kW. In addition, at the maximum output level, the beam quality factor of the Q-switched Ho:SYSO laser is measured to be about 1.6.

We present a planar model system of a silica covered with a monolayer of nonlinear graphene to achieve a tunable Goos–Hänchen (GH) shift in the terahertz range. It is theoretically found that the transition between a negative shift and a large positive one can be realized by altering the intensity of incident light. Moreover, by controlling the chemical potential of graphene and the incident angle of light, we can further control the tunable GH shift dynamically. Numerical simulations for GH shifts based on Gaussian waves are in good agreement with our theoretical calculations.

CONDENSED MATTER: STRUCTURE, MECHANICAL AND THERMAL PROPERTIES

We study the negative thermal expansion (NTE) properties and effect of Na insertion on the NTE of the framework material GaFe(CN)$_{6}$ by first-principles calculations based on density functional theory within the quasi-harmonic approximation. The calculated results show that the material exhibits NTE due to the low transverse vibrational modes of the CN groups. The modes demonstrate larger negative values of the mode Grüneisen parameters. Once Na is introduced in the framework of the material, it prefers to locate at the center of the quadrates of the framework material and binds to the four N anions nearby. As a consequence, the transverse vibrational mode of the CN group is clearly hindered and the NTE of the material is weakened. Our theoretical calculations have clarified the mechanisms of NTE and the effect of the guest Na on the NTE of the framework material.

Structural, thermal expansion, and magnetic properties of the Dy$_{2}$Fe$_{16}$Cr compound are investigated by means of x-ray diffraction and magnetization measurements. The Dy$_{2}$Fe$_{16}$Cr compound has a hexagonal Th$_{2}$Ni$_{17}$-type structure. There exists a negative thermal expansion resulting from a strong spontaneous magnetostriction in the magnetic state of the Dy$_{2}$Fe$_{16}$Cr compound. The average thermal expansion coefficient is $-0.794\times 10^{-5}$/K in the temperature range 292–407 K. The spontaneous magnetostrictive deformation and the Curie temperature are discussed.

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

The electronic structures of Ti$_{2}$NbSb with Hg$_{2}$CuTi structure and TiZrNbSb with LiMgPdSn structure are investigated using first-principles calculations. The results indicate that Ti$_{2}$NbSb is a fully compensated ferrimagnetic spin-gapless semiconductor with an energy gap of 0.13 eV, and TiZrNbSb is a half-metallic fully compensated ferrimagnet with a half-metallic gap of 0.17 eV. For Ti$_{2}$NbSb, the total energy of the Hg$_{2}$CuTi structure is 0.62 eV/f.u. higher than that of the L2$_{1}$ structure, which is the ground state, and for TiZrNbSb, the total energy of the structure considered in this work is only 0.15 eV/f.u. larger than that of the ground state. Thus both of them may be good candidates for spintronic applications.

We report Shubnikov–de Haas (SdH) oscillations of a three-dimensional (3D) Dirac semimetal candidate of layered material ZrTe$_{5}$ single crystals through contactless electron spin resonance (ESR) measurements with the magnetic field up to 1.4 T. The ESR signals manifest remarkably anisotropic characteristics with respect to the direction of the magnetic field, indicating an anisotropic Fermi surface in ZrTe$_{5}$. Further experiments demonstrate that the ZrTe$_{5}$ single crystals have the signature of massless Dirac fermions with nontrivial $\pi$ Berry phase, key evidence for 3D Dirac/Weyl fermions. Moreover, the onset of quantum oscillation of our ZrTe$_{5}$ crystals revealed by the ESR can be derived down to 0.2 T, much smaller than the onset of SdH oscillation determined by conventional magnetoresistance measurements. Therefore, ESR measurement is a powerful tool to study the topologically nontrivial electronic structure in Dirac/Weyl semimetals and other topological materials with low bulk carrier density.

We present a quantum study on the electrical behavior of the self-switching diode (SSD). Our simulation is based on non-equilibrium Green's function formalism along with an atomistic tight-binding model. Using this method, electrical characteristics of devices, such as turn-on voltage, rectification ratio, and differential resistance, are investigated. Also, the effects of geometrical variations on the electrical parameters of SSDs are simulated. The carrier distribution inside the nano-channel is successfully simulated in a two-dimensional model under zero, reverse, and forward bias conditions. The results indicate that the turn-on voltage, rectification ratio, and differential resistance can be optimized by choosing appropriate geometrical parameters.

This work details a study based on HfS$_{2}$ transistors utilizing an n-octadecylphosphonic acid-based self-assembled monolayer (SAM) as the gate dielectric. The fabrication of the SAM-based two-dimensional (2D) material transistor is simple and can be used to improve the quality of the interface of air-sensitive 2D materials. In comparison to HfS$_{2}$ transistors utilizing a conventional Al$_{2}$O$_{3}$ gate insulator by atomic layer deposition, HfS$_{2}$ transistors utilizing an SAM as the gate dielectric can reduce the operation region from 4 V to 2 V, enhance the field-effect mobility from 0.03 cm$^{2}$/Vs to 0.75 cm$^{2}$/Vs, improve the sub-threshold swing from 404 mV/dec to 156 mV/dec, and optimize the hysteresis to 0.03 V, thus demonstrating improved quality of the semiconductor/insulator interface.

We report the temperature, magnetic field and time dependences of magnetization in advanced Ba122 superconducting tapes. The sample exhibits peculiar vortex creep behavior. Below 10 K, the normalized magnetization relaxation rate $S=d\ln(-M)/d\ln(t)$ shows a temperature-insensitive plateau with a value comparable to that of low-temperature superconductors, which can be explained within the framework of collective creep theory. It then enters into a second collective creep regime when the temperature increases. Interestingly, the relaxation rate below 20 K tends to reach saturation with increasing the field. However, it changes to a power law dependence on the field at a higher temperature. A vortex phase diagram composed of the collective and the plastic creep regions is shown. Benefiting from the strong grain boundary pinning, the advanced Ba122 superconducting tape has potential to be applied not only in liquid helium but also in liquid hydrogen or at temperatures accessible with cryocoolers.

High resolution laser-based angle-resolved photoemission measurements are carried out on an overdoped superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ with a $T_{\rm c}$ of 75 K. Two Fermi surface sheets caused by bilayer splitting are clearly identified with rather different doping levels: the bonding sheet corresponds to a doping level of 0.14, which is slightly underdoped while the antibonding sheet has a doping of 0.27 that is heavily overdoped, giving an overall doping level of 0.20 for the sample. Different superconducting gap sizes on the two Fermi surface sheets are revealed. The superconducting gap on the antibonding Fermi surface sheet follows a standard d-wave form while it deviates from the standard d-wave form for the bonding Fermi surface sheet. The maximum gap difference between the two Fermi surface sheets near the antinodal region is $\sim$2 meV. These observations provide important information for studying the relationship between the Fermi surface topology and superconductivity, and the layer-dependent superconductivity in high temperature cuprate superconductors.

The classical frustrated antiferromagnetic $J_1$–$J_2$ model is considered in a description of the classical spin wave for a vector spin system. Its ground state (GS) spin ordering is analyzed by minimizing its energy. Our analytical derivations show that all the spins in the GS phase must lie in planes that are parallel to each other. When applying the derived formulations to concrete lattices such as the square and simple cubic lattices, we find that in the large $J_2$ region, a large continuous GS degeneracy concluded by a qualitative analysis is lifted, and collinear striped ordering is selected as the GS phase.

Off-stoichiometric full-Heusler alloy Co$_{2}$MnAl thin films with different thicknesses are epitaxially grown on GaAs (001) substrates by molecular-beam epitaxy. The composition of the films, close to Co$_{1.65}$Mn$_{1.35}$Al (CMA), is determined by x-ray photoelectron spectroscopy and energy dispersive spectroscopy. Tunable perpendicular magnetic anisotropy (PMA) from 3.41 Merg/cm$^{3}$ to 1.88 Merg/cm$^{3}$ with the thickness increasing from 10 nm to 30 nm is found, attributed to the relaxation of residual compressive strain. Moreover, comparing with the ultrathin CoFeB/MgO used in the conventional perpendicular magnetic tunnel junction, the CMA electrode has a higher magnetic thermal stability with more volume involved. The PMA in CMA films is sustainable up to 300$^{\circ}\!$C, compatible with semiconductor techniques. This work provides a possibility for the development of perpendicular magnetized full-Heusler compounds with high thermal stability and spin polarization.

It has been demonstrated that the zigzag honeycomb nanoribbons exhibit an intriguing edge magnetism. Here the effect of the anisotropy on the edge magnetism in zigzag honeycomb nanoribbons is investigated using two kinds of large-scale quantum Monte Carlo simulations. The anisotropy in zigzag honeycomb nanoribbons is characterized by the ratios of nearest-neighbor hopping integrals $t_{1}$ in one direction and $t_{2}$ in another direction. Considering the electron-electron correlation, it is shown that the edge ferromagnetism could be enhanced greatly as $t_{2}/|t_{1}|$ increases from 1 to 3, which not only presents an avenue for the control of this magnetism but is also useful for exploring further novel magnetism in new nano-scale materials.

Magnetization reversal in magnetic soft/hard bilayer systems is studied analytically by means of a variational method for magnetic energies in a continuum model. The demagnetization curve is involved with nonlinear equations, and the solution is given implicitly in the form of Jacobi functions, which is valid for the total reversal process. Based on the non-trivial solutions, hysteresis loops, as well as the maximum energy product $(BH)_{\max}$ versus thicknesses of soft/hard layers are obtained. With regard to $(BH)_{\max}$, improvement of the remanence competes with loss of coercive force. As a result, an optimum condition exists. For a given thickness of the hard layer, the optimum condition at which the largest $(BH)_{\max}$ could be achieved is discussed, which is slightly different from previous works.

For square-step quantum wells (SSQWs) and graded-step quantum wells (GSQWs), the nonlinear optical rectification (NOR), second harmonic generation (SHG) and third harmonic generation (THG) coefficients under an intense laser field (ILF) are analyzed. The found results indicate that ILF can ensure a vital influence on the shape and height of the confined potential profile of both SSQWs and GSQWs, and alterations of the dipole moment matrix elements and the energy levels are adhered on the profile of the confined potential. According to the results, the potential profile and height of the GSQWs are affected more significantly by ILF intensity compared to SSQWs. These results indicate that NOR, SHG and THG coefficients of SSQWs and GSQWs may be calibrated in a preferred energy range and the magnitude of the resonance peak (RP) by tuning the ILF parameter. It is feasible to classify blue or red shifts in RP locations of NOR, SHG and THG coefficients by varying the ILF parameter. Our results can be useful in investigating new ways of manipulating the opto-electronic properties of semiconductor QW devices.

CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

Growth of high-quality single crystals is of great significance for research of condensed matter physics. The exploration of suitable growing conditions for single crystals is expensive and time-consuming, especially for ternary compounds because of the lack of ternary phase diagram. Here we use machine learning (ML) trained on our experimental data to predict and instruct the growth. Four kinds of ML methods, including support vector machine (SVM), decision tree, random forest and gradient boosting decision tree, are adopted. The SVM method is relatively stable and works well, with an accuracy of 81% in predicting experimental results. By comparison, the accuracy of laboratory reaches 36%. The decision tree model is also used to reveal which features will take critical roles in growing processes.

Silicon on insulator with highly uniform top Si is fabricated by co-implantation of H$^{+}$ and He$^{+}$ ions. Compared with the conventional ion-slicing process with H implantation only, the co-implanted specimens whose He depth is deeper than H profile have the top Si layer with better uniformity after splitting. In addition, the splitting occurs at the position that the maximum concentration peak of H overlaps with the secondary concentration peak of He after annealing. It is suggested that the H/He co-implantation technology is a promising approach for fabricating fully depleted silicon on insulator.